Question

Simplify -4x^3 *2y^-2 *5y^5 * x^-8

Answer 1

Collect like terms 
so take it in steps :
1) -4x^3 * x^-8 . rules of powers state that when you are multiplying like terms(both have to do with x) you can add the powers. thus = -4x^-5
2) 2y^-2 * 5y^5 . same rule as above. since -2+5=3. the number before your coefficient (x or y) tells you how many lots of it you have . the answer becomes 2*5y^3 = 10y^3 .
3) since you are now left with x and y s which are not the same number, you can multiply out ---> 10*-4 = -40 
                          ---> y^3*x^-5 stays the same as you can not combine y and x
In total you have : -40y^3*x^-5